Edge-preserving filtering by projection onto L0 gradient constraint

We propose an edge-preserving filtering method with a novel use of the L0 gradient. Our method, termed as the L0 gradient projection, is formulated as the minimization of a quadratic data-fidelity to an input image subject to the constraint that theL0 gradient, the number of non-zero gradients, of the output image is less than a user-given parameter α. This strategy is much more intuitive than the conventional approach, the L0 gradient minimization, that minimizes the sum of the L0 gradient plus the quadratic data-fidelity, because one can directly impose a desired degree of flatness by α, which is impossible in the L0 gradient minimization. We also provide an efficient algorithm based on the so-called alternating direction method of multipliers for solving the nonconvex optimization problem associated with the L0 gradient projection. The utility of the L0 gradient projection is illustrated by experiments.